Zeta and q-Zeta Functions and Associated Series and Integrals
- 1st Edition - October 11, 2011
- Latest edition
- Authors: Hari M Srivastava, Junesang Choi
- Language: English
Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions… Read more
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Description
Description
Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals.
Key features
Key features
- Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
Readership
Readership
Researchers, lecturers and postgraduate students in the fields of mathematical and applied sciences
Table of contents
Table of contents
Preface
Acknowledgements
1. Introduction and Preliminaries
1.1 Gamma and Beta Functions
1.2 The Euler-Mascheroni Constant γ
1.3 Polygamma Functions
1.4 The Multiple Gamma Functions
1.5 The Gaussian Hypergeometric Function and its Generalization
1.6 Stirling Numbers of the First and Second Kind
1.7 Bernoulli, Euler and Genocchi Polynomials and Numbers
1.8 Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials and Numbers
1.9 Inequalities for the Gamma Function and the Double Gamma Function
Problems
2. The Zeta and Related Functions
2.1 Multiple Hurwitz Zeta Functions
2.2 The Hurwitz (or Generalized) Zeta Function
2.3 The Riemann Zeta Function
2.4 Polylogarithm Functions
2.5 Hurwitz–Lerch Zeta Functions
2.6 Generalizations of the Hurwitz–Lerch Zeta Function
2.7 Analytic Continuations of Multiple Zeta Functions
Problems
3. Series Involving Zeta Functions
3.1 Historical Introduction
3.2 Use of the Binomial Theorem
3.3 Use of Generating Functions
3.4 Use of Multiple Gamma Functions
Problems
4. Evaluations and Series Representations
4.1 Evaluation of
4.2 Rapidly Convergent Series for
4.3 Further Series Representations
4.4 Computational Results
Problems
5. Determinants of the Laplacians
5.1 The n-Dimensional Problem
5.2 Computations Using the Simple and Multiple Gamma Functions
5.3 Computations Using Series of Zeta Functions
5.4 Computations using Zeta Regularized Products
5.5 Remarks and Observations
Problems
6. q-Extensions of Some Special Functions and Polynomials
6.1 q-Shifted Factorials and q-Binomial Coefficients
6.2 q-Derivative, q-Antiderivative and Jackson q-Integral
6.3 q-Binomial Theorem
6.4 q-Gamma Function and q-Beta Function
6.5 A q-Extension of the Multiple Gamma Functions
6.6 q-Bernoulli Numbers and q-Bernoulli Polynomials
6.7 q-Euler Numbers and q-Euler Polynomials
6.8 The q-Apostol-Bernoulli Polynomials of Order
6.9 The q-Apostol-Euler Polynomials of Order
6.10 A Generalized q-Zeta Function
6.11 Multiple q-Zeta Functions
Problems
7. Miscellaneous Results
7.1 A Set of Useful Mathematical Constants
7.2 Log-Sine Integrals Involving Series Associated with the Zeta Function and Polylogarithms
7.3 Applications of the Gamma and Polygamma Functions Involving Convolutions of the Rayleigh Functions
7.4 Bernoulli and Euler Polynomials at Rational Arguments
7.5 Closed-Form Summation of Trigonometric Series
Problems
Bibliography
Review quotes
Review quotes
"Overall this is a very valuable reference for those with an interest in the Riemann zeta function or who have occasion to evaluate series involving the zeta function."—BookInspections.com, May 2013
"Overall this is a very valuable reference for those with an interest in the Riemann zeta function or who have occasion to evaluate series involving the zeta function."—Zentralblatt MATH 2012
Product details
Product details
- Edition: 1
- Latest edition
- Published: October 11, 2011
- Language: English
About the authors
About the authors
HS
Hari M Srivastava
Dr. Hari M. Srivastava is Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria, British Columbia, Canada. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur, India. Dr. Srivastava has held (and continues to hold) numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in different parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many Special Issues of scientific research journals as the Lead or Joint Guest Editor, including the MDPI journal Axioms, Mathematics, and Symmetry, the Elsevier journals, Journal of Computational and Applied Mathematics, Applied Mathematics and Computation, Chaos, Solitons & Fractals, Alexandria Engineering Journal, and Journal of King Saud University – Science, the Wiley journal, Mathematical Methods in the Applied Sciences, the Springer journals, Advances in Difference Equations, Journal of Inequalities and Applications, Fixed Point Theory and Applications, and Boundary Value Problems, the American Institute of Physics journal, Chaos: An Interdisciplinary Journal of Nonlinear Science, and the American Institute of Mathematical Sciences journal, AIMS Mathematics, among many others. Dr. Srivastava has been a Clarivate Analytics (Web of Science) Highly-Cited Researcher since 2015. Dr. Srivastava’s research interests include several areas of Pure and Applied Mathematical Sciences, such as Real and Complex Analysis, Fractional Calculus and Its Applications, Integral Equations and Transforms, Higher Transcendental Functions and Their Applications, q-Series and q-Polynomials, Analytic Number Theory, Analytic and Geometric Inequalities, Probability and Statistics, and Inventory Modeling and Optimization. He has published 36 books, monographs, and edited volumes, 36 book (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1450 peer-reviewed international scientific research journal articles, as well as Forewords and Prefaces to many books and journals.
JC